Krispy Kreme ice cream -- or cereal?

Krispy Kreme's new CEO knows the brand has a great big, gooey gap to fill.

But how do you move the chain beyond the doughnut — after 77 years — when the doughnut, and nothing but the doughnut, got you to where you are?

That's the question that Tony Thompson, who took over as CEO last month, must answer.

In a phone interview with USA TODAY along with the company's executive chairman, James Morgan, Thompson indicates he has plans to leverage cravings for its doughnuts as a springboard to other stuff. Think savory lunch offerings — such as sandwiches served on something sweet. Think licensed products, including ice cream. Think of Krispy Kreme-branded coffee sold in all sorts of places and formats.

"You have a big advantage when you have an iconic, craveable brand," says Thompson, 47, who most recently was chief operating officer at the Papa John's pizza chain. "Krispy Kreme can leverage this in ways other brands can't."

For Krispy Kreme, whose growth, stock price and public image have been on a harrowing roller coaster ride over the past few decades, it's all about finding a new, corporate sweet spot. (Its stock was trading on Thursday at $15.61, near the 52-week low of $15.42.) Doughnuts, alone, just won't cut the mustard in a world where Starbucks serves fancy-dancy salads and Dunkin' Donuts serves bacon ranch chicken sandwiches.

"Everyone loves the Krispy Kreme brand, but no one wants to eat a doughnut," says Jason Wright, group strategy director at the VIA Agency. "It has huge brand awareness — but not a lot of brand relevance."

Thompson aims to change that. Doughnuts, he insists, still will be at the center of the plate. But he hopes to enlarge the scope of the plate to have room for other strategic options.

Among his plans are more:

• Limited-time offers. Few things do better on social media — and attract Millennials— than unusual, limited-time doughnut offers. So, Thompson says, he hopes to do more of them — like the current Brownie Batter Doughnut and Birthday Cake Batter Doughnut. "The connection to these on social media can be very emotional," he says.

Friday's 77th Birthday promo is bound to generate buzz: Buy a dozen doughnuts and get a second dozen for 77 cents.

• Product licensing. Sweet products such as candies, cereals, ice cream and even cake mixes could be future licensing ventures for Krispy Kreme, he says. All of these are within "the wheelhouse of our brand," says Thompson.

• Coffee products. Krispy Kreme already sells bagged coffee in some retail outlets, but it recently signed an agreement with Green Mountain to launch Krispy Kreme coffees, Smooth and Decaf, in K-Cup packs for Keurig brewers by the end of 2014.

• Options beyond breakfast. While there are no plans to sell a burger between two halves of a Krispy Kreme doughnut, as some ballparks and state fairs already do, there is ongoing research into "savory" lunchtime offerings that would have a Krispy Kreme touch, Thompson says. These might be sandwiches, but he declined to be specific.

The company also wants to create more "snackable" offerings that would drive consumers in between 11 a.m. and 4 p.m., when business tends to be slowest, says Morgan.

• Healthy products. Maybe some baked items along with the fried, says Thompson. But he promises no more whole wheat doughnuts, which were a total bust in 2007.

• Beverages. Beyond coffee and its line of Chiller drinks, Thompson plans to expand and refocus on beverages, though he declined to be specific. "Beverage is a big, big opportunity for us," he says.

• More stores. About 600 of the chain's 860 stores are outside the U.S. Many domestic locations closed from 2005 to 2008, when the company's stock collapsed after too many larger, expensive stores were built too quickly. Future stores will be smaller, says Thompson. The company plans to open up to 80 outside the U.S. this year and up to 15 in the U.S., he says.

Although Thompson comes from a pizza background, he says he has no plans to sell pizza at Krispy Kreme. But delivery of Krispy Kreme products is something that could be tested, he says, "though it's not at the top of my list."